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arXiv:0905.2039 · Physical Review B

Generalized quantum dimer model applied to the frustrated Heisenberg model on the square lattice: Emergence of a mixed columnar-plaquette phase

Arnaud Ralko, Matthieu Mambrini, Didier Poilblanc

Published Nov 30, 2009• 39 citations
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Abstract

Aiming to describe frustrated quantum magnets with nonmagnetic singlet ground states, we have extended the Rokhsar-Kivelson (RK) loop expansion to derive a generalized quantum dimer model containing only connected terms up to arbitrary order. For the square-lattice frustrated Heisenberg antiferromagnet (${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ model), an expansion up to eighth order shows that the leading correction to the original RK model comes from dimer moves on length-6 loops. This model free of the original sign problem is treated by advanced numerical techniques. The results suggest that a rotationally anisotropic plaquette phase [A. Ralko, D. Poilblanc, and R. Moessner, Phys. Rev. Lett. 100, 037201 (2008)] is the ground state of the Heisenberg model in the parameter region of maximum frustration.

DOI
10.1103/physrevb.80.184427

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Aiming to describe frustrated quantum magnets with nonmagnetic singlet ground states, we have extended the Rokhsar-Kivelson (RK) loop expansion to derive a generalized quantum dimer model containing only connected terms up to arbitrary order. For the square-lattice frustrated Heisenberg antiferromagnet (J1\ensuremath-J2\ensuremath-J3{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}J1​\ensuremath-J2​\ensuremath-J3​ model), an expansion up to eighth order shows that the leading correction to the original RK model comes from dimer moves on length-6 loops. This model free of the original sign problem is treated by advanced numerical techniques. The results suggest that a rotationally anisotropic plaquette phase [A. Ralko, D. Poilblanc, and R. Moessner, Phys. Rev. Lett. 100, 037201 (2008)] is the ground state of the Heisenberg model in the parameter region of maximum frustration.
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